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fredd [130]
3 years ago
8

) It has been estimated that 53% of all college students change their major at least once during the course of their college car

eer. Suppose you are told that the sample proportion for a random sample was 0.48. Furthermore, you are told that the probability of geing a sample proportion of this size or smaller is 14%. What must have been the sample size?
Mathematics
1 answer:
Ymorist [56]3 years ago
6 0

Answer:

116 students

Step-by-step explanation:

The standard deviation for a proportion is:

s=\sqrt{\frac{(1-p)*p}{n}}

For any measured sample proportion x, the z score is given by:

z = \frac{x-p}{s}

The population proportion is 0.53

At the 14th percentile, the corresponding z-score is z =-1.08.

Since 0.48 is at the 14th percentile, the standard deviation is:

-1.08=\frac{0.48-0.53}{s}\\ s=0.46296

Therefore, the sample size 'n' is given by:

0.046296=\sqrt{\frac{(1-0.53)*0.53}{n}}\\n=\frac{0.47*0.53}{0.046296^2}\\n= 116\  students

The sample size must have been of 116 students.

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